[logic-ml] Kobe Colloquium (talk by Dmitri Shakhmatov)

[Joerg Brendle]

Kobe Colloquium on Logic, Statistics and Informatics

以下の要領でコロクウィウムを開催します。

日時：2010年12月16日（木）15:10 〜
場所：神戸大学自然科学総合研究棟3号館4階421室（渕野グループプレゼンテーション室）
講演者：Dmitri Shakhmatov（愛媛大学）
題目：A Kronecker-Weyl theorem for subsets of abelian groups

アブストラクト：
Let N be the set of non-negative integer numbers, T the circle group and c
the cardinality of the continuum.
Given an abelian group G of size at most 2^c and a countable family F of
infinite subsets of G,
we construct ``Baire many'' monomorphisms pi: G to T ^c such that pi(E) is
dense in { y in T^c : ny=0 }
whenever n in N , E in F, nE = {0} and { x in E : mx=g } is finite for all g
in G and m such that
n = mk for some k in  N \ {1} . We apply this result to obtain an algebraic
description of countable
potentially dense subsets of abelian groups, thereby making a significant
progress towards a
solution of a problem of Markov going back to 1944. A particular case of our
result yields a
positive answer to a problem of Tkachenko and Yaschenko (2002). Applications
to group actions and
discrete flows on T^cont, diophantine approximation, Bohr topologies and
Bohr compactifications
are also provided.

交通：阪急六甲駅またはJR六甲道駅から神戸市バス36系統「鶴甲団地」
行きに乗車，「神大本部工学部前」停留所下車，徒歩すぐ．
http://www.kobe-u.ac.jp/info/access/rokko/rokkodai-dai2.htm

連絡先：ブレンドレ ヨーグ  brendle at kurt.scitec.kobe-u.ac.jp
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